| Summary: | In this paper, using the concept of multi-pomeron exchange, we develope a Monte Carlo model of interacting quark–gluon strings acting as particle-emitting sources aimed at describing inelastic proton–proton interactions at high energies. The implemented 3D (three-dimensional) dynamics of colour string formation resulted in their finite length in the rapidity space and in the fluctuating event-by-event spatial density. Thus, this results in string cluster formation because of the fusion mechanism and the appearance of long-range multiplicity and mean transverse momentum (mean-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula>) correlations in rapidity. We study, via the pseudorapidity dependence, the sensitivity to the details of the 3D dynamical formation of strings for several observables such as the forward–backward correlation coefficient value, strongly intensive quantity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Σ</mi></semantics></math></inline-formula>, and the “almost” strongly intensive observable, the variance, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>σ</mi><mi>C</mi><mn>2</mn></msubsup></semantics></math></inline-formula>, of the distribution of the asymmetry coefficient, <i>C</i>. The strongly intensive quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Σ</mi></semantics></math></inline-formula> is used in this study to suppress trivial statistical fluctuations in the number of particles emitting similar types of sources and to reveal the intrinsic fluctuations of a single source. We demonstrate the connection between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Σ</mi></semantics></math></inline-formula> and such often used observables as cumulants, factorial cumulants, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>σ</mi><mi>C</mi><mn>2</mn></msubsup></semantics></math></inline-formula>. We stress the importance of the contribution of “short” strings and the event asymmetry of the initial conditions on the long-range correlation measures. We argue that string cluster formation because of the fusion mechanism explains the collective effects seen in multiplicity and transverse momentum–multiplicity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>⟨</mo><msub><mi>p</mi><mi>T</mi></msub><mo>⟩</mo></mrow></semantics></math></inline-formula>–<i>N</i>, long-range correlation functions.
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